In addition to being a complete and utter
net.kook on
sci.math, Alexander Abian would also provide
useful information on that same
newsfroup! His examples on how replacing some
axioms of very simple theories of sets (limited versions of
set theory) were somewhat simplistic, but often
interesting. He also helped many a
poster with understanding various
fixed point properties; his still-extant
homepage gives a "
universal" fixed point
theorem (he calls it "most
fundamental") that doesn't require a
topology or
ordering on the set.
1
Truly an interesting person!
- He uses ordinals to analyse the structure of iteration of a map on a set; you might consider the order (and induced topology) "cheating", in that they impose structure on the set. However, this structure is natural.